Square - Octagon - Circle - Modelling puzzle
in my opinion you are going fine, remember that there are many ways to achieve what you want in Blender, so in this case I see two other possibilities.

Option one: 

You can add the flat base geometry.



Select and erase these vertices



Add a mirror modifier like this





And then extrude





Option Two:

Use Boolean

Add a cube



Add a 8 vertices cylinder



Add a Boolean modifier to the cube like this



To look the cylinder in wireframe only, go to Object menu > Display > and set Maximum Draw Type to Wire



Repeat the previous steps with the other geometry, at the end you will have something like this



Now when you're ok with the look, just apply the modifiers and done.